Fastest way to snap two faces together by aligning their centers in non-standard orientations?
When you have the two objects with the origins in the same location, activate snap vertex option, select the object that needs to rotate and press R, searching for a vertex of the angled face.

If the rotation is not aligned with a view, use custom orientations, and press R followed by the choosen axis twice (i.e. R,X,X will rotate around X local axis).